### On Simultaneous Approximation and Combinations of Lupas Type Operators

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**Authors:**T. A. K. SINHA, K. K. SINGH AND A. K. SHARMA

**DOI:**10.46793/KgJMat2105.761B

**Abstract:**

This work deals with the BVP multi-point existence of solutions of a nonlinear fractional diﬀerential equations at resonance, where the kernel’s dimension of the fractional diﬀerential operator is equal to three. Our results are based on Mawhin’s theory of coincidence. As application, we give an example to illustrate our results.

**Keywords:**

Fractional diﬀerential equations, fractional Caputo derivative, multi-point boundary value problem, resonance, three dimensional kernels, coincidence degree theory.

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